Since the Rindler chart is a coordinate chart for Minkowski spacetime, we expect to find ten linearly independent Killing vector fields.
12.
The twist vector measures the extent to which the Killing vector fails to be orthogonal to a family of 3-surfaces.
13.
If the spacetime supports a Killing vector field tangent to a circle, then the angular momentum about the axis is conserved.
14.
This is always a Lie group, and as usual it is easier to classify the underlying Lie algebras of Killing vector fields.
15.
Examples of such are fully general Petrov type I spacetimes with no Killing vectors, see Coley " et al . " below.
16.
Some of the most important vector fields are Killing vector fields which are those spacetime symmetries that preserve the underlying metric structure of a manifold.
17.
In rough terms, Killing vector fields preserve the distance between any two points of the manifold and often go by the name of isometries.
18.
If X is a Killing vector field and Y is a harmonic vector field, then g ( X, Y ) is a harmonic function.
19.
When the energy-momentum tensor represents a perfect fluid, every Killing vector field preserves the energy density, pressure and the fluid flow vector field.
20.
Another observation is that unless the background metric tensor has a global timelike Killing vector, there is no way to define a vacuum or ground state canonically.
